--- /dev/null
+Thu Mar 2 08:40:33 WST 2006 John Darrington <john@darrington.wattle.id.au>
+
+ * Moved files from src directory
--- /dev/null
+## Process this file with automake to produce Makefile.in -*- makefile -*-
+
+src/math/linreg/%: AM_CPPFLAGS += \
+ -I$(top_srcdir)/src/data \
+ -I$(top_srcdir)/src/math \
+ -I$(top_srcdir)/lib/linreg
+
+
+noinst_LIBRARIES += src/math/linreg/libpspp_linreg.a
+
+src_math_linreg_libpspp_linreg_a_SOURCES = \
+ src/math/linreg/coefficient.c \
+ src/math/linreg/coefficient.h \
+ src/math/linreg/linreg.c \
+ src/math/linreg/linreg.h
--- /dev/null
+/* lib/linreg/coefficient.c
+
+ Copyright (C) 2005 Free Software Foundation, Inc.
+ Written by Jason H Stover.
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2 of the License, or (at
+ your option) any later version.
+
+ This program is distributed in the hope that it will be useful, but
+ WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
+ 02111-1307, USA.
+ */
+
+/*
+ Accessor functions for matching coefficients and variables.
+ */
+#include <assert.h>
+#include "coefficient.h"
+#include "linreg.h"
+#include "src/math/design-matrix.h"
+#include "src/data/variable.h"
+#include "src/data/value.h"
+
+#include <gl/xalloc.h>
+
+
+struct varinfo
+{
+ const struct variable *v; /* Variable associated with this
+ coefficient. Note this variable may not
+ be unique. In other words, a
+ coefficient structure may have other
+ v_info's, each with its own variable.
+ */
+ const union value *val; /* Value of the variable v which this
+ varinfo refers to. This member is relevant
+ only to categorical variables.
+ */
+};
+
+void pspp_linreg_coeff_free (struct pspp_linreg_coeff *c)
+{
+ free (c);
+}
+
+/*
+ Initialize the variable and value pointers inside the
+ coefficient structures for the linear model.
+ */
+void
+pspp_linreg_coeff_init (pspp_linreg_cache *c, struct design_matrix *X)
+{
+ size_t i;
+ size_t j;
+ int n_vals = 1;
+ struct pspp_linreg_coeff *coeff;
+
+ c->coeff =
+ xnmalloc (X->m->size2 + 1,
+ sizeof (*c->coeff));
+ for (i = 0; i < X->m->size2; i++)
+ {
+ j = i + 1; /* The first coefficient is the intercept. */
+ coeff = c->coeff + j;
+ coeff->n_vars = n_vals; /* Currently, no procedures allow interactions.
+ This will have to change when procedures that
+ allow interaction terms are written.
+ */
+ coeff->v_info = xnmalloc (coeff->n_vars, sizeof (*coeff->v_info));
+ assert (coeff->v_info != NULL);
+ coeff->v_info->v = (const struct variable *) design_matrix_col_to_var (X, i);
+
+ if (coeff->v_info->v->type == ALPHA)
+ {
+ size_t k;
+ k = design_matrix_var_to_column (X, coeff->v_info->v);
+ assert (k <= i);
+ k = i - k;
+ coeff->v_info->val = cat_subscript_to_value (k, (struct variable *) coeff->v_info->v);
+ }
+ }
+}
+void
+pspp_linreg_coeff_set_estimate (struct pspp_linreg_coeff *c,
+ double estimate)
+{
+ c->estimate = estimate;
+}
+void
+pspp_linreg_coeff_set_std_err (struct pspp_linreg_coeff *c,
+ double std_err)
+{
+ c->std_err = std_err;
+}
+/*
+ How many variables are associated with this coefficient?
+ */
+int
+pspp_linreg_coeff_get_n_vars (struct pspp_linreg_coeff *c)
+{
+ return c->n_vars;
+}
+/*
+ Which variable does this coefficient match?
+ */
+const struct variable *
+pspp_linreg_coeff_get_var (struct pspp_linreg_coeff *c, int i)
+{
+ assert (i < c->n_vars);
+ return (c->v_info + i)->v;
+}
+/*
+ Which value is associated with this coefficient/variable comination?
+*/
+const union value *
+pspp_linreg_coeff_get_value (struct pspp_linreg_coeff *c,
+ const struct variable *v)
+{
+ int i = 0;
+ const struct variable *candidate;
+
+ while (i < c->n_vars)
+ {
+ candidate = pspp_linreg_coeff_get_var (c, i);
+ if (v->index == candidate->index)
+ {
+ return (c->v_info + i)->val;
+ }
+ i++;
+ }
+ return NULL;
+}
--- /dev/null
+/* lib/linreg/coefficient.c
+
+ Copyright (C) 2005 Free Software Foundation, Inc.
+ Written by Jason H Stover.
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2 of the License, or (at
+ your option) any later version.
+
+ This program is distributed in the hope that it will be useful, but
+ WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
+ 02111-1307, USA.
+ */
+
+
+#ifndef COEFFICIENT_H
+#define COEFFICIENT_H
+
+
+#include "linreg.h"
+
+struct design_matrix;
+
+/*
+ Cache for the relevant data from the model. There are several
+ members which the caller might not use, and which could use a lot of
+ storage. Therefore non-essential members of the struct will be
+ allocated only when requested.
+ */
+struct pspp_linreg_coeff
+{
+ double estimate; /* Estimated coefficient. */
+ double std_err; /* Standard error of the estimate. */
+ struct varinfo *v_info; /* Information pertaining to the
+ variable(s) associated with this
+ coefficient. The calling function
+ should initialize this value with the
+ functions in coefficient.c. The
+ estimation procedure ignores this
+ member. It is here so the caller can
+ match parameters with relevant variables
+ and values. If the coefficient is
+ associated with an interaction, then
+ v_info contains information for multiple
+ variables.
+ */
+ int n_vars; /* Number of variables associated with this coefficient.
+ Coefficients corresponding to interaction terms will
+ have more than one variable.
+ */
+};
+
+
+
+/*
+ Accessor functions for matching coefficients and variables.
+ */
+
+void pspp_linreg_coeff_free (struct pspp_linreg_coeff *c);
+
+/*
+ Initialize the variable and value pointers inside the
+ coefficient structures for the linear model.
+ */
+void
+pspp_linreg_coeff_init (pspp_linreg_cache *c,
+ struct design_matrix *X);
+
+
+void
+pspp_linreg_coeff_set_estimate (struct pspp_linreg_coeff *c,
+ double estimate);
+
+void
+pspp_linreg_coeff_set_std_err (struct pspp_linreg_coeff *c,
+ double std_err);
+/*
+ How many variables are associated with this coefficient?
+ */
+int
+pspp_linreg_coeff_get_n_vars (struct pspp_linreg_coeff *c);
+
+/*
+ Which variable does this coefficient match?
+ */
+const struct variable *
+pspp_linreg_coeff_get_var (struct pspp_linreg_coeff *c, int i);
+
+/*
+ Which value is associated with this coefficient/variable comination?
+*/
+const union value *
+pspp_linreg_coeff_get_value (struct pspp_linreg_coeff *c,
+ const struct variable *v);
+
+
+#endif
--- /dev/null
+/* lib/linreg/linreg.c
+
+ Copyright (C) 2005 Free Software Foundation, Inc.
+ Written by Jason H. Stover.
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2 of the License, or (at
+ your option) any later version.
+
+ This program is distributed in the hope that it will be useful, but
+ WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
+ 02111-1307, USA.
+*/
+
+#include <gsl/gsl_fit.h>
+#include <gsl/gsl_multifit.h>
+
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_cblas.h>
+
+
+
+/*
+ Find the least-squares estimate of b for the linear model:
+
+ Y = Xb + Z
+
+ where Y is an n-by-1 column vector, X is an n-by-p matrix of
+ independent variables, b is a p-by-1 vector of regression coefficients,
+ and Z is an n-by-1 normally-distributed random vector with independent
+ identically distributed components with mean 0.
+
+ This estimate is found via the sweep operator or singular-value
+ decomposition with gsl.
+
+
+ References:
+
+ 1. Matrix Computations, third edition. GH Golub and CF Van Loan.
+ The Johns Hopkins University Press. 1996. ISBN 0-8018-5414-8.
+
+ 2. Numerical Analysis for Statisticians. K Lange. Springer. 1999.
+ ISBN 0-387-94979-8.
+
+ 3. Numerical Linear Algebra for Applications in Statistics. JE Gentle.
+ Springer. 1998. ISBN 0-387-98542-5.
+*/
+
+#include "linreg.h"
+#include "coefficient.h"
+#include "sweep.h"
+#include <gsl/gsl_errno.h>
+/*
+ Get the mean and standard deviation of a vector
+ of doubles via a form of the Kalman filter as
+ described on page 32 of [3].
+ */
+static int
+linreg_mean_std (gsl_vector_const_view v, double *mp, double *sp, double *ssp)
+{
+ size_t i;
+ double j = 0.0;
+ double d;
+ double tmp;
+ double mean;
+ double variance;
+
+ mean = gsl_vector_get (&v.vector, 0);
+ variance = 0;
+ for (i = 1; i < v.vector.size; i++)
+ {
+ j = (double) i + 1.0;
+ tmp = gsl_vector_get (&v.vector, i);
+ d = (tmp - mean) / j;
+ mean += d;
+ variance += j * (j - 1.0) * d * d;
+ }
+ *mp = mean;
+ *sp = sqrt (variance / (j - 1.0));
+ *ssp = variance;
+
+ return GSL_SUCCESS;
+}
+
+/*
+ Allocate a pspp_linreg_cache and return a pointer
+ to it. n is the number of cases, p is the number of
+ independent variables.
+ */
+pspp_linreg_cache *
+pspp_linreg_cache_alloc (size_t n, size_t p)
+{
+ pspp_linreg_cache *c;
+
+ c = (pspp_linreg_cache *) malloc (sizeof (pspp_linreg_cache));
+ c->indep_means = gsl_vector_alloc (p);
+ c->indep_std = gsl_vector_alloc (p);
+ c->ssx = gsl_vector_alloc (p); /* Sums of squares for the independent
+ variables.
+ */
+ c->ss_indeps = gsl_vector_alloc (p); /* Sums of squares for the model
+ parameters.
+ */
+ c->cov = gsl_matrix_alloc (p + 1, p + 1); /* Covariance matrix. */
+ c->n_obs = n;
+ c->n_indeps = p;
+ /*
+ Default settings.
+ */
+ c->method = PSPP_LINREG_SWEEP;
+
+ return c;
+}
+
+void
+pspp_linreg_cache_free (pspp_linreg_cache * c)
+{
+ gsl_vector_free (c->indep_means);
+ gsl_vector_free (c->indep_std);
+ gsl_vector_free (c->ss_indeps);
+ gsl_matrix_free (c->cov);
+ pspp_linreg_coeff_free (c->coeff);
+ free (c);
+}
+
+/*
+ Fit the linear model via least squares. All pointers passed to pspp_linreg
+ are assumed to be allocated to the correct size and initialized to the
+ values as indicated by opts.
+ */
+int
+pspp_linreg (const gsl_vector * Y, const gsl_matrix * X,
+ const pspp_linreg_opts * opts, pspp_linreg_cache * cache)
+{
+ int rc;
+ gsl_matrix *design;
+ gsl_matrix_view xtx;
+ gsl_matrix_view xm;
+ gsl_matrix_view xmxtx;
+ gsl_vector_view xty;
+ gsl_vector_view xi;
+ gsl_vector_view xj;
+ gsl_vector *param_estimates;
+
+ size_t i;
+ size_t j;
+ double tmp;
+ double m;
+ double s;
+ double ss;
+
+ if (cache == NULL)
+ {
+ return GSL_EFAULT;
+ }
+ if (opts->get_depvar_mean_std)
+ {
+ linreg_mean_std (gsl_vector_const_subvector (Y, 0, Y->size),
+ &m, &s, &ss);
+ cache->depvar_mean = m;
+ cache->depvar_std = s;
+ cache->sst = ss;
+ }
+ for (i = 0; i < cache->n_indeps; i++)
+ {
+ if (opts->get_indep_mean_std[i])
+ {
+ linreg_mean_std (gsl_matrix_const_column (X, i), &m, &s, &ss);
+ gsl_vector_set (cache->indep_means, i, m);
+ gsl_vector_set (cache->indep_std, i, s);
+ gsl_vector_set (cache->ssx, i, ss);
+ }
+ }
+ cache->dft = cache->n_obs - 1;
+ cache->dfm = cache->n_indeps;
+ cache->dfe = cache->dft - cache->dfm;
+ cache->n_coeffs = X->size2 + 1; /* Adjust this later to allow for regression
+ through the origin.
+ */
+ if (cache->method == PSPP_LINREG_SWEEP)
+ {
+ gsl_matrix *sw;
+ /*
+ Subtract the means to improve the condition of the design
+ matrix. This requires copying X and Y. We do not divide by the
+ standard deviations of the independent variables here since doing
+ so would cause a miscalculation of the residual sums of
+ squares. Dividing by the standard deviation is done GSL's linear
+ regression functions, so if the design matrix has a poor
+ condition, use QR decomposition.
+
+ The design matrix here does not include a column for the intercept
+ (i.e., a column of 1's). If using PSPP_LINREG_QR, we need that column,
+ so design is allocated here when sweeping, or below if using QR.
+ */
+ design = gsl_matrix_alloc (X->size1, X->size2);
+ for (i = 0; i < X->size2; i++)
+ {
+ m = gsl_vector_get (cache->indep_means, i);
+ for (j = 0; j < X->size1; j++)
+ {
+ tmp = (gsl_matrix_get (X, j, i) - m);
+ gsl_matrix_set (design, j, i, tmp);
+ }
+ }
+ sw = gsl_matrix_calloc (cache->n_indeps + 1, cache->n_indeps + 1);
+ xtx = gsl_matrix_submatrix (sw, 0, 0, cache->n_indeps, cache->n_indeps);
+
+ for (i = 0; i < xtx.matrix.size1; i++)
+ {
+ tmp = gsl_vector_get (cache->ssx, i);
+ gsl_matrix_set (&(xtx.matrix), i, i, tmp);
+ xi = gsl_matrix_column (design, i);
+ for (j = (i + 1); j < xtx.matrix.size2; j++)
+ {
+ xj = gsl_matrix_column (design, j);
+ gsl_blas_ddot (&(xi.vector), &(xj.vector), &tmp);
+ gsl_matrix_set (&(xtx.matrix), i, j, tmp);
+ }
+ }
+
+ gsl_matrix_set (sw, cache->n_indeps, cache->n_indeps, cache->sst);
+ xty = gsl_matrix_column (sw, cache->n_indeps);
+ /*
+ This loop starts at 1, with i=0 outside the loop, so we can get
+ the model sum of squares due to the first independent variable.
+ */
+ xi = gsl_matrix_column (design, 0);
+ gsl_blas_ddot (&(xi.vector), Y, &tmp);
+ gsl_vector_set (&(xty.vector), 0, tmp);
+ tmp *= tmp / gsl_vector_get (cache->ssx, 0);
+ gsl_vector_set (cache->ss_indeps, 0, tmp);
+ for (i = 1; i < cache->n_indeps; i++)
+ {
+ xi = gsl_matrix_column (design, i);
+ gsl_blas_ddot (&(xi.vector), Y, &tmp);
+ gsl_vector_set (&(xty.vector), i, tmp);
+ }
+
+ /*
+ Sweep on the matrix sw, which contains XtX, XtY and YtY.
+ */
+ reg_sweep (sw);
+ cache->sse = gsl_matrix_get (sw, cache->n_indeps, cache->n_indeps);
+ cache->mse = cache->sse / cache->dfe;
+ /*
+ Get the intercept.
+ */
+ m = cache->depvar_mean;
+ for (i = 0; i < cache->n_indeps; i++)
+ {
+ tmp = gsl_matrix_get (sw, i, cache->n_indeps);
+ cache->coeff[i + 1].estimate = tmp;
+ m -= tmp * gsl_vector_get (cache->indep_means, i);
+ }
+ /*
+ Get the covariance matrix of the parameter estimates.
+ Only the upper triangle is necessary.
+ */
+
+ /*
+ The loops below do not compute the entries related
+ to the estimated intercept.
+ */
+ for (i = 0; i < cache->n_indeps; i++)
+ for (j = i; j < cache->n_indeps; j++)
+ {
+ tmp = -1.0 * cache->mse * gsl_matrix_get (sw, i, j);
+ gsl_matrix_set (cache->cov, i + 1, j + 1, tmp);
+ }
+ /*
+ Get the covariances related to the intercept.
+ */
+ xtx = gsl_matrix_submatrix (sw, 0, 0, cache->n_indeps, cache->n_indeps);
+ xmxtx = gsl_matrix_submatrix (cache->cov, 0, 1, 1, cache->n_indeps);
+ xm = gsl_matrix_view_vector (cache->indep_means, 1, cache->n_indeps);
+ rc = gsl_blas_dsymm (CblasRight, CblasUpper, cache->mse,
+ &xtx.matrix, &xm.matrix, 0.0, &xmxtx.matrix);
+ if (rc == GSL_SUCCESS)
+ {
+ tmp = cache->mse / cache->n_obs;
+ for (i = 1; i < 1 + cache->n_indeps; i++)
+ {
+ tmp -= gsl_matrix_get (cache->cov, 0, i)
+ * gsl_vector_get (cache->indep_means, i - 1);
+ }
+ gsl_matrix_set (cache->cov, 0, 0, tmp);
+
+ cache->coeff[0].estimate = m;
+ }
+ else
+ {
+ fprintf (stderr, "%s:%d:gsl_blas_dsymm: %s\n",
+ __FILE__, __LINE__, gsl_strerror (rc));
+ exit (rc);
+ }
+ gsl_matrix_free (sw);
+ }
+ else
+ {
+ /*
+ Use QR decomposition via GSL.
+ */
+
+ param_estimates = gsl_vector_alloc (1 + X->size2);
+ design = gsl_matrix_alloc (X->size1, 1 + X->size2);
+
+ for (j = 0; j < X->size1; j++)
+ {
+ gsl_matrix_set (design, j, 0, 1.0);
+ for (i = 0; i < X->size2; i++)
+ {
+ tmp = gsl_matrix_get (X, j, i);
+ gsl_matrix_set (design, j, i + 1, tmp);
+ }
+ }
+ gsl_multifit_linear_workspace *wk =
+ gsl_multifit_linear_alloc (design->size1, design->size2);
+ rc = gsl_multifit_linear (design, Y, param_estimates,
+ cache->cov, &(cache->sse), wk);
+ for (i = 0; i < cache->n_coeffs; i++)
+ {
+ cache->coeff[i].estimate = gsl_vector_get (param_estimates, i);
+ }
+ if (rc == GSL_SUCCESS)
+ {
+ gsl_multifit_linear_free (wk);
+ gsl_vector_free (param_estimates);
+ }
+ else
+ {
+ fprintf (stderr, "%s:%d: gsl_multifit_linear returned %d\n",
+ __FILE__, __LINE__, rc);
+ }
+ }
+
+
+ cache->ssm = cache->sst - cache->sse;
+ /*
+ Get the remaining sums of squares for the independent
+ variables.
+ */
+ m = 0;
+ for (i = 1; i < cache->n_indeps; i++)
+ {
+ j = i - 1;
+ m += gsl_vector_get (cache->ss_indeps, j);
+ tmp = cache->ssm - m;
+ gsl_vector_set (cache->ss_indeps, i, tmp);
+ }
+
+ gsl_matrix_free (design);
+ return GSL_SUCCESS;
+}
--- /dev/null
+/* lib/linreg/linreg.h
+
+ Copyright (C) 2005 Free Software Foundation, Inc.
+ Written by Jason H. Stover.
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2 of the License, or (at
+ your option) any later version.
+
+ This program is distributed in the hope that it will be useful, but
+ WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
+ 02111-1307, USA.
+*/
+
+#ifndef LINREG_H
+#define LINREG_H
+
+
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+
+struct variable ;
+struct pspp_linreg_coeff;
+
+
+enum
+{
+ PSPP_LINREG_SWEEP,
+ PSPP_LINREG_SVD
+};
+
+
+
+/*
+ Options describing what special values should be computed.
+ */
+struct pspp_linreg_opts_struct
+{
+ int resid; /* Should the residuals be returned? */
+
+ int get_depvar_mean_std;
+ int *get_indep_mean_std; /* Array of booleans dictating which
+ independent variables need their means
+ and standard deviations computed within
+ pspp_linreg. This array MUST be of
+ length n_indeps. If element i is 1,
+ pspp_linreg will compute the mean and
+ variance of indpendent variable i. If
+ element i is 0, it will not compute the
+ mean and standard deviation, and assume
+ the values are stored.
+ cache->indep_mean[i] is the mean and
+ cache->indep_std[i] is the sample
+ standard deviation.
+ */
+};
+typedef struct pspp_linreg_opts_struct pspp_linreg_opts;
+
+
+/*
+ Find the least-squares estimate of b for the linear model:
+
+ Y = Xb + Z
+
+ where Y is an n-by-1 column vector, X is an n-by-p matrix of
+ independent variables, b is a p-by-1 vector of regression coefficients,
+ and Z is an n-by-1 normally-distributed random vector with independent
+ identically distributed components with mean 0.
+
+ This estimate is found via the sweep operator or singular-value
+ decomposition with gsl.
+
+
+ References:
+
+ 1. Matrix Computations, third edition. GH Golub and CF Van Loan.
+ The Johns Hopkins University Press. 1996. ISBN 0-8018-5414-8.
+
+ 2. Numerical Analysis for Statisticians. K Lange. Springer. 1999.
+ ISBN 0-387-94979-8.
+
+ 3. Numerical Linear Algebra for Applications in Statistics. JE Gentle.
+ Springer. 1998. ISBN 0-387-98542-5.
+*/
+
+
+struct pspp_linreg_cache_struct
+{
+ int n_obs; /* Number of observations. */
+ int n_indeps; /* Number of independent variables. */
+ int n_coeffs;
+
+ /*
+ The variable struct is ignored during estimation.
+ It is here so the calling procedure can
+ find the variable used in the model.
+ */
+ const struct variable *depvar;
+
+ gsl_vector *residuals;
+ struct pspp_linreg_coeff *coeff;
+ int method; /* Method to use to estimate parameters. */
+ /*
+ Means and standard deviations of the variables.
+ If these pointers are null when pspp_linreg() is
+ called, pspp_linreg() will compute their values.
+
+ Entry i of indep_means is the mean of independent
+ variable i, whose observations are stored in the ith
+ column of the design matrix.
+ */
+ double depvar_mean;
+ double depvar_std;
+ gsl_vector *indep_means;
+ gsl_vector *indep_std;
+
+ /*
+ Sums of squares.
+ */
+ double ssm; /* Sums of squares for the overall model. */
+ gsl_vector *ss_indeps; /* Sums of squares from each
+ independent variable.
+ */
+ double sst; /* Sum of squares total. */
+ double sse; /* Sum of squares error. */
+ double mse; /* Mean squared error. This is just sse / dfe, but
+ since it is the best unbiased estimate of the population
+ variance, it has its own entry here.
+ */
+ gsl_vector *ssx; /* Centered sums of squares for independent variables,
+ i.e. \sum (x[i] - mean(x))^2.
+ */
+ double ssy; /* Centered sums of squares for dependent variable. */
+ /*
+ Covariance matrix of the parameter estimates.
+ */
+ gsl_matrix *cov;
+ /*
+ Degrees of freedom.
+ */
+ double dft;
+ double dfe;
+ double dfm;
+
+ /*
+ 'Hat' or Hessian matrix, i.e. (X'X)^{-1}, where X is our
+ design matrix.
+ */
+ gsl_matrix *hat;
+};
+
+typedef struct pspp_linreg_cache_struct pspp_linreg_cache;
+
+
+
+/*
+ Allocate a pspp_linreg_cache and return a pointer
+ to it. n is the number of cases, p is the number of
+ independent variables.
+ */
+pspp_linreg_cache * pspp_linreg_cache_alloc (size_t n, size_t p);
+
+void pspp_linreg_cache_free (pspp_linreg_cache * c);
+
+/*
+ Fit the linear model via least squares. All pointers passed to pspp_linreg
+ are assumed to be allocated to the correct size and initialized to the
+ values as indicated by opts.
+ */
+int pspp_linreg (const gsl_vector * Y, const gsl_matrix * X,
+ const pspp_linreg_opts * opts,
+ pspp_linreg_cache * cache);
+
+
+#endif
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